Last updated: 2022-02-13

Checks: 5 1

Knit directory: Padgett-Dissertation/

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# Load packages
source("code/load_packages.R")
source("code/load_utility_functions.R")
# environment options
options(scipen = 999, digits=3)

# results folder
res_folder <- paste0(w.d, "/data/study_2")

# read in data
source("code/load_extracted_data.R")

Convergence

This is component of the project, a coarse grain investigation of the posteriors’ convergence will be assessed. In the proposal, I stated that I will evaluate convergence of the posteriors using the R-hat value as measures of convergence. R-hat values close to 1, within 0.1, will be considered a “converged” posterior for the parameter.

The code below loops through the posterior summaries to identify converged solutions.

mydata <- mydata %>%
  # group by condition, iteration, and parameter group to get Rhat more summarised
  group_by(condition, iter, parameter_group) %>%
  mutate(Rhat_paragrp = mean(Rhat)) %>%
  ungroup() %>%
  mutate(
    converge = ifelse(Rhat - 1.10 < 0, 1, 0),
    converge_paragrp = ifelse(Rhat_paragrp - 1.10 < 0, 1, 0)
  ) %>%
  group_by(condition, iter, parameter_group) %>%
  mutate(
     converge_proportion_paragrp = sum(converge)/n(),
  )

# Update condition labels for plotting
mydata$condition_lbs <- factor(
  mydata$condition, 
  levels = 1:24,
  labels = c(
    "nCat=2, nItem=  5, N=  500",
    "nCat=2, nItem=  5, N=2500",
    "nCat=2, nItem=10, N=  500",
    "nCat=2, nItem=10, N=2500",
    "nCat=2, nItem=20, N=  500",
    "nCat=2, nItem=20, N=2500",
    "nCat=5, nItem=  5, N=  500",
    "nCat=5, nItem=  5, N=2500",
    "nCat=5, nItem=10, N=  500",
    "nCat=5, nItem=10, N=2500",
    "nCat=5, nItem=20, N=  500",
    "nCat=5, nItem=20, N=2500",
    "nCat=3, nItem=  5, N=  500",
    "nCat=3, nItem=  5, N=2500",
    "nCat=3, nItem=10, N=  500",
    "nCat=3, nItem=10, N=2500",
    "nCat=3, nItem=20, N=  500",
    "nCat=3, nItem=20, N=2500",
    "nCat=7, nItem=  5, N=  500",
    "nCat=7, nItem=  5, N=2500",
    "nCat=7, nItem=10, N=  500",
    "nCat=7, nItem=10, N=2500",
    "nCat=7, nItem=20, N=  500",
    "nCat=7, nItem=20, N=2500"
  )
)

# columns to keep
keep_cols <- c("condition","condition_lbs", "iter", "N", "N_items", "N_cat", "parameter_group", "Rhat_paragrp", "converge_paragrp")

Summaring Convergence

Factor Loadings (\(\lambda\))

param = "FACTOR LOADING"

conv <- mydata %>%
  filter(parameter_group == "lambda")

conv_para_grp <- mydata %>%
  filter(parameter_group == "lambda") %>%
  select(all_of(keep_cols)) %>%
  distinct()

# tabular summary
conv_tbl <- conv %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	500	341	0.682
2	2	5	2500	500	327	0.654
3	2	10	500	1000	846	0.846
4	2	10	2500	1000	900	0.900
5	2	20	500	2000	1898	0.949
6	2	20	2500	2000	1945	0.973
7	5	5	500	500	388	0.776
8	5	5	2500	500	456	0.912
9	5	10	500	1000	920	0.920
10	5	10	2500	1000	965	0.965
11	5	20	500	2000	1890	0.945
12	5	20	2500	2000	1933	0.967
13	3	5	500	500	433	0.866
14	3	5	2500	500	474	0.948
15	3	10	500	1000	980	0.980
16	3	10	2500	1000	995	0.995
17	3	20	500	2000	1987	0.994
18	3	20	2500	2000	2000	1.000
19	7	5	500	500	389	0.778
20	7	5	2500	250	207	0.828
21	7	10	500	500	424	0.848
22	7	10	2500	500	451	0.902
23	7	20	500	1000	879	0.879
24	7	20	2500	760	700	0.921

conv_grp_tbl <- conv_para_grp %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge_paragrp),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_grp_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	69	0.69
2	2	5	2500	100	56	0.56
3	2	10	500	100	97	0.97
4	2	10	2500	100	99	0.99
5	2	20	500	100	100	1.00
6	2	20	2500	100	100	1.00
7	5	5	500	100	89	0.89
8	5	5	2500	100	99	0.99
9	5	10	500	100	100	1.00
10	5	10	2500	100	100	1.00
11	5	20	500	100	100	1.00
12	5	20	2500	100	100	1.00
13	3	5	500	100	90	0.90
14	3	5	2500	100	100	1.00
15	3	10	500	100	100	1.00
16	3	10	2500	100	100	1.00
17	3	20	500	100	100	1.00
18	3	20	2500	100	100	1.00
19	7	5	500	100	87	0.87
20	7	5	2500	50	48	0.96
21	7	10	500	50	50	1.00
22	7	10	2500	50	50	1.00
23	7	20	500	50	50	1.00
24	7	20	2500	38	38	1.00

# visualize Rhat values
conv_grp <- conv %>%
  select(condition_lbs, iter, N_cat, N_items, N, Rhat_paragrp, converge_paragrp) %>%
  distinct()

Adding missing grouping variables: `condition`, `parameter_group`

ggplot() +
  geom_violin(data=conv, aes(x=condition_lbs , y=Rhat, group=condition))+
  geom_jitter(data=conv_grp, aes(x=condition_lbs , y=Rhat_paragrp), color="red", alpha=0.75)+
  geom_abline(intercept = 1.10, slope=0, linetype="dashed")+
  coord_flip()+
  labs(
    title=paste0("Estimates of Rhat for ", param, " posteriors" ),
    subtitle ="Plot includes Rhat for each parameter estimate (violin plot) and\n average Rhat of all similar parameters (e.g., all loadings)",
    caption = "Note. Dashed line represent Rhat = 1.10 for a 'converged' posterior"
  ) +
  theme_bw()+
  theme(
    panel.grid = element_blank()
  )

Item Thresholds (\(\tau\))

param = "Item Thresholds"

conv <- mydata %>%
  filter(parameter_group == "tau")

conv_para_grp <- mydata %>%
  filter(parameter_group == "tau") %>%
  select(all_of(keep_cols)) %>%
  distinct()

# tabular summary
conv_tbl <- conv %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	500	478	0.956
2	2	5	2500	500	491	0.982
3	2	10	500	1000	985	0.985
4	2	10	2500	1000	1000	1.000
5	2	20	500	2000	2000	1.000
6	2	20	2500	2000	2000	1.000
7	5	5	500	2000	1943	0.972
8	5	5	2500	2000	1997	0.999
9	5	10	500	4000	3980	0.995
10	5	10	2500	4000	3998	1.000
11	5	20	500	8000	7970	0.996
12	5	20	2500	8000	7990	0.999
13	3	5	500	1000	977	0.977
14	3	5	2500	1000	1000	1.000
15	3	10	500	2000	1997	0.999
16	3	10	2500	2000	2000	1.000
17	3	20	500	4000	4000	1.000
18	3	20	2500	4000	4000	1.000
19	7	5	500	3000	2854	0.951
20	7	5	2500	1500	1483	0.989
21	7	10	500	3000	2971	0.990
22	7	10	2500	3000	2989	0.996
23	7	20	500	6000	5933	0.989
24	7	20	2500	4560	4538	0.995

conv_grp_tbl <- conv_para_grp %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge_paragrp),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_grp_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	97	0.97
2	2	5	2500	100	100	1.00
3	2	10	500	100	100	1.00
4	2	10	2500	100	100	1.00
5	2	20	500	100	100	1.00
6	2	20	2500	100	100	1.00
7	5	5	500	100	100	1.00
8	5	5	2500	100	100	1.00
9	5	10	500	100	100	1.00
10	5	10	2500	100	100	1.00
11	5	20	500	100	100	1.00
12	5	20	2500	100	100	1.00
13	3	5	500	100	100	1.00
14	3	5	2500	100	100	1.00
15	3	10	500	100	100	1.00
16	3	10	2500	100	100	1.00
17	3	20	500	100	100	1.00
18	3	20	2500	100	100	1.00
19	7	5	500	100	100	1.00
20	7	5	2500	50	50	1.00
21	7	10	500	50	50	1.00
22	7	10	2500	50	50	1.00
23	7	20	500	50	50	1.00
24	7	20	2500	38	38	1.00

# visualize Rhat values
conv_grp <- conv %>%
  select(condition_lbs, iter, N_cat, N_items, N, Rhat_paragrp, converge_paragrp) %>%
  distinct()

Adding missing grouping variables: `condition`, `parameter_group`

ggplot() +
  geom_violin(data=conv, aes(x=condition_lbs , y=Rhat, group=condition))+
  geom_jitter(data=conv_grp, aes(x=condition_lbs , y=Rhat_paragrp), color="red", alpha=0.75)+
  geom_abline(intercept = 1.10, slope=0, linetype="dashed")+
  coord_flip()+
  labs(
    title=paste0("Estimates of Rhat for ", param, " posteriors" ),
    subtitle ="Plot includes Rhat for each parameter estimate (violin plot) and\n average Rhat of all similar parameters (e.g., all loadings)",
    caption = "Note. Dashed line represent Rhat = 1.10 for a 'converged' posterior"
  ) +
  theme_bw()+
  theme(
    panel.grid = element_blank()
  )

Latent Response Variance (\(\theta\))

param = "Latent Response Variance"

conv <- mydata %>%
  filter(parameter_group == "theta")

conv_para_grp <- mydata %>%
  filter(parameter_group == "theta") %>%
  select(all_of(keep_cols)) %>%
  distinct()

# tabular summary
conv_tbl <- conv %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	500	250	0.500
2	2	5	2500	500	310	0.620
3	2	10	500	1000	756	0.756
4	2	10	2500	1000	887	0.887
5	2	20	500	2000	1844	0.922
6	2	20	2500	2000	1941	0.971
7	5	5	500	500	366	0.732
8	5	5	2500	500	452	0.904
9	5	10	500	1000	908	0.908
10	5	10	2500	1000	964	0.964
11	5	20	500	2000	1876	0.938
12	5	20	2500	2000	1932	0.966
13	3	5	500	500	402	0.804
14	3	5	2500	500	465	0.930
15	3	10	500	1000	976	0.976
16	3	10	2500	1000	993	0.993
17	3	20	500	2000	1986	0.993
18	3	20	2500	2000	2000	1.000
19	7	5	500	500	374	0.748
20	7	5	2500	250	205	0.820
21	7	10	500	500	420	0.840
22	7	10	2500	500	451	0.902
23	7	20	500	1000	861	0.861
24	7	20	2500	760	700	0.921

conv_grp_tbl <- conv_para_grp %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge_paragrp),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_grp_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	33	0.33
2	2	5	2500	100	46	0.46
3	2	10	500	100	85	0.85
4	2	10	2500	100	99	0.99
5	2	20	500	100	100	1.00
6	2	20	2500	100	100	1.00
7	5	5	500	100	82	0.82
8	5	5	2500	100	99	0.99
9	5	10	500	100	100	1.00
10	5	10	2500	100	100	1.00
11	5	20	500	100	100	1.00
12	5	20	2500	100	100	1.00
13	3	5	500	100	82	0.82
14	3	5	2500	100	100	1.00
15	3	10	500	100	100	1.00
16	3	10	2500	100	100	1.00
17	3	20	500	100	100	1.00
18	3	20	2500	100	100	1.00
19	7	5	500	100	79	0.79
20	7	5	2500	50	48	0.96
21	7	10	500	50	50	1.00
22	7	10	2500	50	50	1.00
23	7	20	500	50	50	1.00
24	7	20	2500	38	38	1.00

# visualize Rhat values
conv_grp <- conv %>%
  select(condition_lbs, iter, N_cat, N_items, N, Rhat_paragrp, converge_paragrp) %>%
  distinct()

Adding missing grouping variables: `condition`, `parameter_group`

ggplot() +
  geom_violin(data=conv, aes(x=condition_lbs , y=Rhat, group=condition))+
  geom_jitter(data=conv_grp, aes(x=condition_lbs , y=Rhat_paragrp), color="red", alpha=0.75)+
  geom_abline(intercept = 1.10, slope=0, linetype="dashed")+
  coord_flip()+
  labs(
    title=paste0("Estimates of Rhat for ", param, " posteriors" ),
    subtitle ="Plot includes Rhat for each parameter estimate (violin plot) and\n average Rhat of all similar parameters (e.g., all loadings)",
    caption = "Note. Dashed line represent Rhat = 1.10 for a 'converged' posterior"
  ) +
  theme_bw()+
  theme(
    panel.grid = element_blank()
  )

Response Time Intercepts (\(\beta_{lrt}\))

param = "RT Intercepts"

conv <- mydata %>%
  filter(parameter_group == "beta_lrt")

conv_para_grp <- mydata %>%
  filter(parameter_group == "beta_lrt") %>%
  select(all_of(keep_cols)) %>%
  distinct()

# tabular summary
conv_tbl <- conv %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	500	402	0.804
2	2	5	2500	500	401	0.802
3	2	10	500	1000	927	0.927
4	2	10	2500	1000	974	0.974
5	2	20	500	2000	1986	0.993
6	2	20	2500	2000	1999	1.000
7	5	5	500	500	464	0.928
8	5	5	2500	500	488	0.976
9	5	10	500	1000	984	0.984
10	5	10	2500	1000	1000	1.000
11	5	20	500	2000	1995	0.998
12	5	20	2500	2000	2000	1.000
13	3	5	500	500	480	0.960
14	3	5	2500	500	494	0.988
15	3	10	500	1000	996	0.996
16	3	10	2500	1000	1000	1.000
17	3	20	500	2000	2000	1.000
18	3	20	2500	2000	2000	1.000
19	7	5	500	500	482	0.964
20	7	5	2500	250	237	0.948
21	7	10	500	500	497	0.994
22	7	10	2500	500	497	0.994
23	7	20	500	1000	999	0.999
24	7	20	2500	760	760	1.000

conv_grp_tbl <- conv_para_grp %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge_paragrp),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_grp_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	85	0.85
2	2	5	2500	100	81	0.81
3	2	10	500	100	96	0.96
4	2	10	2500	100	100	1.00
5	2	20	500	100	100	1.00
6	2	20	2500	100	100	1.00
7	5	5	500	100	97	0.97
8	5	5	2500	100	99	0.99
9	5	10	500	100	100	1.00
10	5	10	2500	100	100	1.00
11	5	20	500	100	100	1.00
12	5	20	2500	100	100	1.00
13	3	5	500	100	99	0.99
14	3	5	2500	100	100	1.00
15	3	10	500	100	100	1.00
16	3	10	2500	100	100	1.00
17	3	20	500	100	100	1.00
18	3	20	2500	100	100	1.00
19	7	5	500	100	98	0.98
20	7	5	2500	50	50	1.00
21	7	10	500	50	50	1.00
22	7	10	2500	50	50	1.00
23	7	20	500	50	50	1.00
24	7	20	2500	38	38	1.00

# visualize Rhat values
conv_grp <- conv %>%
  select(condition_lbs, iter, N_cat, N_items, N, Rhat_paragrp, converge_paragrp) %>%
  distinct()

Adding missing grouping variables: `condition`, `parameter_group`

ggplot() +
  geom_violin(data=conv, aes(x=condition_lbs , y=Rhat, group=condition))+
  geom_jitter(data=conv_grp, aes(x=condition_lbs , y=Rhat_paragrp), color="red", alpha=0.75)+
  geom_abline(intercept = 1.10, slope=0, linetype="dashed")+
  coord_flip()+
  labs(
    title=paste0("Estimates of Rhat for ", param, " posteriors" ),
    subtitle ="Plot includes Rhat for each parameter estimate (violin plot) and\n average Rhat of all similar parameters (e.g., all loadings)",
    caption = "Note. Dashed line represent Rhat = 1.10 for a 'converged' posterior"
  ) +
  theme_bw()+
  theme(
    panel.grid = element_blank()
  )

Response Time Precision (\(\sigma_{lrt}\))

param = "RT Precision"

conv <- mydata %>%
  filter(parameter_group == "sigma_lrt")

conv_para_grp <- mydata %>%
  filter(parameter_group == "sigma_lrt") %>%
  select(all_of(keep_cols)) %>%
  distinct()

# tabular summary
conv_tbl <- conv %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	500	485	0.970
2	2	5	2500	500	497	0.994
3	2	10	500	1000	998	0.998
4	2	10	2500	1000	1000	1.000
5	2	20	500	2000	2000	1.000
6	2	20	2500	2000	2000	1.000
7	5	5	500	500	500	1.000
8	5	5	2500	500	500	1.000
9	5	10	500	1000	1000	1.000
10	5	10	2500	1000	1000	1.000
11	5	20	500	2000	2000	1.000
12	5	20	2500	2000	2000	1.000
13	3	5	500	500	499	0.998
14	3	5	2500	500	500	1.000
15	3	10	500	1000	1000	1.000
16	3	10	2500	1000	1000	1.000
17	3	20	500	2000	2000	1.000
18	3	20	2500	2000	2000	1.000
19	7	5	500	500	500	1.000
20	7	5	2500	250	250	1.000
21	7	10	500	500	500	1.000
22	7	10	2500	500	500	1.000
23	7	20	500	1000	1000	1.000
24	7	20	2500	760	760	1.000

conv_grp_tbl <- conv_para_grp %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge_paragrp),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_grp_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	100	1
2	2	5	2500	100	100	1
3	2	10	500	100	100	1
4	2	10	2500	100	100	1
5	2	20	500	100	100	1
6	2	20	2500	100	100	1
7	5	5	500	100	100	1
8	5	5	2500	100	100	1
9	5	10	500	100	100	1
10	5	10	2500	100	100	1
11	5	20	500	100	100	1
12	5	20	2500	100	100	1
13	3	5	500	100	100	1
14	3	5	2500	100	100	1
15	3	10	500	100	100	1
16	3	10	2500	100	100	1
17	3	20	500	100	100	1
18	3	20	2500	100	100	1
19	7	5	500	100	100	1
20	7	5	2500	50	50	1
21	7	10	500	50	50	1
22	7	10	2500	50	50	1
23	7	20	500	50	50	1
24	7	20	2500	38	38	1

# visualize Rhat values
conv_grp <- conv %>%
  select(condition_lbs, iter, N_cat, N_items, N, Rhat_paragrp, converge_paragrp) %>%
  distinct()

Adding missing grouping variables: `condition`, `parameter_group`

ggplot() +
  geom_violin(data=conv, aes(x=condition_lbs , y=Rhat, group=condition))+
  geom_jitter(data=conv_grp, aes(x=condition_lbs , y=Rhat_paragrp), color="red", alpha=0.75)+
  geom_abline(intercept = 1.10, slope=0, linetype="dashed")+
  coord_flip()+
  labs(
    title=paste0("Estimates of Rhat for ", param, " posteriors" ),
    subtitle ="Plot includes Rhat for each parameter estimate (violin plot) and\n average Rhat of all similar parameters (e.g., all loadings)",
    caption = "Note. Dashed line represent Rhat = 1.10 for a 'converged' posterior"
  ) +
  theme_bw()+
  theme(
    panel.grid = element_blank()
  )

Response Time Factor Precision (\(\sigma_s\))

param = "Speed LV Precision"

conv <- mydata %>%
  filter(parameter_group == "sigma_s")

conv_para_grp <- mydata %>%
  filter(parameter_group == "sigma_s") %>%
  select(all_of(keep_cols)) %>%
  distinct()

# tabular summary
conv_tbl <- conv %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	99	0.99
2	2	5	2500	100	97	0.97
3	2	10	500	100	100	1.00
4	2	10	2500	100	100	1.00
5	2	20	500	100	100	1.00
6	2	20	2500	100	100	1.00
7	5	5	500	100	100	1.00
8	5	5	2500	100	100	1.00
9	5	10	500	100	100	1.00
10	5	10	2500	100	100	1.00
11	5	20	500	100	100	1.00
12	5	20	2500	100	100	1.00
13	3	5	500	100	100	1.00
14	3	5	2500	100	100	1.00
15	3	10	500	100	100	1.00
16	3	10	2500	100	100	1.00
17	3	20	500	100	100	1.00
18	3	20	2500	100	100	1.00
19	7	5	500	100	100	1.00
20	7	5	2500	50	50	1.00
21	7	10	500	50	50	1.00
22	7	10	2500	50	50	1.00
23	7	20	500	50	50	1.00
24	7	20	2500	38	38	1.00

conv_grp_tbl <- conv_para_grp %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge_paragrp),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_grp_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	99	0.99
2	2	5	2500	100	97	0.97
3	2	10	500	100	100	1.00
4	2	10	2500	100	100	1.00
5	2	20	500	100	100	1.00
6	2	20	2500	100	100	1.00
7	5	5	500	100	100	1.00
8	5	5	2500	100	100	1.00
9	5	10	500	100	100	1.00
10	5	10	2500	100	100	1.00
11	5	20	500	100	100	1.00
12	5	20	2500	100	100	1.00
13	3	5	500	100	100	1.00
14	3	5	2500	100	100	1.00
15	3	10	500	100	100	1.00
16	3	10	2500	100	100	1.00
17	3	20	500	100	100	1.00
18	3	20	2500	100	100	1.00
19	7	5	500	100	100	1.00
20	7	5	2500	50	50	1.00
21	7	10	500	50	50	1.00
22	7	10	2500	50	50	1.00
23	7	20	500	50	50	1.00
24	7	20	2500	38	38	1.00

# visualize Rhat values
conv_grp <- conv %>%
  select(condition_lbs, iter, N_cat, N_items, N, Rhat_paragrp, converge_paragrp) %>%
  distinct()

Adding missing grouping variables: `condition`, `parameter_group`

ggplot() +
  geom_violin(data=conv, aes(x=condition_lbs , y=Rhat, group=condition))+
  geom_jitter(data=conv_grp, aes(x=condition_lbs , y=Rhat_paragrp), color="red", alpha=0.75)+
  geom_abline(intercept = 1.10, slope=0, linetype="dashed")+
  coord_flip()+
  labs(
    title=paste0("Estimates of Rhat for ", param, " posteriors" ),
    subtitle ="Plot includes Rhat for each parameter estimate (violin plot) and\n average Rhat of all similar parameters (e.g., all loadings)",
    caption = "Note. Dashed line represent Rhat = 1.10 for a 'converged' posterior"
  ) +
  theme_bw()+
  theme(
    panel.grid = element_blank()
  )

Factor Covariance (\(\sigma_{st}\))

param = "Latent Covariance"

conv <- mydata %>%
  filter(parameter_group == "sigma_st")

conv_para_grp <- mydata %>%
  filter(parameter_group == "sigma_st") %>%
  select(all_of(keep_cols)) %>%
  distinct()

# tabular summary
conv_tbl <- conv %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	95	0.95
2	2	5	2500	100	98	0.98
3	2	10	500	100	100	1.00
4	2	10	2500	100	100	1.00
5	2	20	500	100	100	1.00
6	2	20	2500	100	100	1.00
7	5	5	500	100	98	0.98
8	5	5	2500	100	100	1.00
9	5	10	500	100	100	1.00
10	5	10	2500	100	100	1.00
11	5	20	500	100	100	1.00
12	5	20	2500	100	100	1.00
13	3	5	500	100	100	1.00
14	3	5	2500	100	100	1.00
15	3	10	500	100	100	1.00
16	3	10	2500	100	100	1.00
17	3	20	500	100	100	1.00
18	3	20	2500	100	100	1.00
19	7	5	500	100	100	1.00
20	7	5	2500	50	50	1.00
21	7	10	500	50	50	1.00
22	7	10	2500	50	50	1.00
23	7	20	500	50	50	1.00
24	7	20	2500	38	38	1.00

conv_grp_tbl <- conv_para_grp %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge_paragrp),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_grp_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	95	0.95
2	2	5	2500	100	98	0.98
3	2	10	500	100	100	1.00
4	2	10	2500	100	100	1.00
5	2	20	500	100	100	1.00
6	2	20	2500	100	100	1.00
7	5	5	500	100	98	0.98
8	5	5	2500	100	100	1.00
9	5	10	500	100	100	1.00
10	5	10	2500	100	100	1.00
11	5	20	500	100	100	1.00
12	5	20	2500	100	100	1.00
13	3	5	500	100	100	1.00
14	3	5	2500	100	100	1.00
15	3	10	500	100	100	1.00
16	3	10	2500	100	100	1.00
17	3	20	500	100	100	1.00
18	3	20	2500	100	100	1.00
19	7	5	500	100	100	1.00
20	7	5	2500	50	50	1.00
21	7	10	500	50	50	1.00
22	7	10	2500	50	50	1.00
23	7	20	500	50	50	1.00
24	7	20	2500	38	38	1.00

# visualize Rhat values
conv_grp <- conv %>%
  select(condition_lbs, iter, N_cat, N_items, N, Rhat_paragrp, converge_paragrp) %>%
  distinct()

Adding missing grouping variables: `condition`, `parameter_group`

ggplot() +
  geom_violin(data=conv, aes(x=condition_lbs , y=Rhat, group=condition))+
  geom_jitter(data=conv_grp, aes(x=condition_lbs , y=Rhat_paragrp), color="red", alpha=0.75)+
  geom_abline(intercept = 1.10, slope=0, linetype="dashed")+
  coord_flip()+
  labs(
    title=paste0("Estimates of Rhat for ", param, " posteriors" ),
    subtitle ="Plot includes Rhat for each parameter estimate (violin plot) and\n average Rhat of all similar parameters (e.g., all loadings)",
    caption = "Note. Dashed line represent Rhat = 1.10 for a 'converged' posterior"
  ) +
  theme_bw()+
  theme(
    panel.grid = element_blank()
  )

PID Relationship (\(\rho\))

param = "PID Relationship"

conv <- mydata %>%
  filter(parameter_group == "rho")

conv_para_grp <- mydata %>%
  filter(parameter_group == "rho") %>%
  select(all_of(keep_cols)) %>%
  distinct()

# tabular summary
conv_tbl <- conv %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	82	0.82
2	2	5	2500	100	80	0.80
3	2	10	500	100	85	0.85
4	2	10	2500	100	97	0.97
5	2	20	500	100	97	0.97
6	2	20	2500	100	100	1.00
7	5	5	500	100	91	0.91
8	5	5	2500	100	97	0.97
9	5	10	500	100	94	0.94
10	5	10	2500	100	100	1.00
11	5	20	500	100	98	0.98
12	5	20	2500	100	100	1.00
13	3	5	500	100	97	0.97
14	3	5	2500	100	98	0.98
15	3	10	500	100	99	0.99
16	3	10	2500	100	100	1.00
17	3	20	500	100	99	0.99
18	3	20	2500	100	100	1.00
19	7	5	500	100	87	0.87
20	7	5	2500	50	45	0.90
21	7	10	500	50	49	0.98
22	7	10	2500	50	49	0.98
23	7	20	500	50	50	1.00
24	7	20	2500	38	38	1.00

conv_grp_tbl <- conv_para_grp %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge_paragrp),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_grp_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	82	0.82
2	2	5	2500	100	80	0.80
3	2	10	500	100	85	0.85
4	2	10	2500	100	97	0.97
5	2	20	500	100	97	0.97
6	2	20	2500	100	100	1.00
7	5	5	500	100	91	0.91
8	5	5	2500	100	97	0.97
9	5	10	500	100	94	0.94
10	5	10	2500	100	100	1.00
11	5	20	500	100	98	0.98
12	5	20	2500	100	100	1.00
13	3	5	500	100	97	0.97
14	3	5	2500	100	98	0.98
15	3	10	500	100	99	0.99
16	3	10	2500	100	100	1.00
17	3	20	500	100	99	0.99
18	3	20	2500	100	100	1.00
19	7	5	500	100	87	0.87
20	7	5	2500	50	45	0.90
21	7	10	500	50	49	0.98
22	7	10	2500	50	49	0.98
23	7	20	500	50	50	1.00
24	7	20	2500	38	38	1.00

# visualize Rhat values
conv_grp <- conv %>%
  select(condition_lbs, iter, N_cat, N_items, N, Rhat_paragrp, converge_paragrp) %>%
  distinct()

Adding missing grouping variables: `condition`, `parameter_group`

ggplot() +
  geom_violin(data=conv, aes(x=condition_lbs , y=Rhat, group=condition))+
  geom_jitter(data=conv_grp, aes(x=condition_lbs , y=Rhat_paragrp), color="red", alpha=0.75)+
  geom_abline(intercept = 1.10, slope=0, linetype="dashed")+
  coord_flip()+
  labs(
    title=paste0("Estimates of Rhat for ", param, " posteriors" ),
    subtitle ="Plot includes Rhat for each parameter estimate (violin plot) and\n average Rhat of all similar parameters (e.g., all loadings)",
    caption = "Note. Dashed line represent Rhat = 1.10 for a 'converged' posterior"
  ) +
  theme_bw()+
  theme(
    panel.grid = element_blank()
  )

Factor Reliability (\(\omega\))

param = "RELIABILITY"

conv <- mydata %>%
  filter(parameter_group == "omega")

conv_para_grp <- mydata %>%
  filter(parameter_group == "omega") %>%
  select(all_of(keep_cols)) %>%
  distinct()

# tabular summary
conv_tbl <- conv %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	63	0.63
2	2	5	2500	100	78	0.78
3	2	10	500	100	88	0.88
4	2	10	2500	100	97	0.97
5	2	20	500	100	96	0.96
6	2	20	2500	100	100	1.00
7	5	5	500	100	87	0.87
8	5	5	2500	100	99	0.99
9	5	10	500	100	95	0.95
10	5	10	2500	100	97	0.97
11	5	20	500	100	98	0.98
12	5	20	2500	100	99	0.99
13	3	5	500	100	89	0.89
14	3	5	2500	100	100	1.00
15	3	10	500	100	100	1.00
16	3	10	2500	100	100	1.00
17	3	20	500	100	100	1.00
18	3	20	2500	100	99	0.99
19	7	5	500	100	81	0.81
20	7	5	2500	50	43	0.86
21	7	10	500	50	46	0.92
22	7	10	2500	50	49	0.98
23	7	20	500	50	49	0.98
24	7	20	2500	38	38	1.00

conv_grp_tbl <- conv_para_grp %>%
  group_by(condition, N_cat, N_items, N) %>%
  summarise(Max_Converged=n(),
            Obs_Converged=sum(converge_paragrp),
            Prop_Converged=Obs_Converged/Max_Converged)

`summarise()` has grouped output by 'condition', 'N_cat', 'N_items'. You can override using the `.groups` argument.

kable(conv_grp_tbl, format="html", digits=3) %>%
  kable_styling(full_width = T)

condition	N_cat	N_items	N	Max_Converged	Obs_Converged	Prop_Converged
1	2	5	500	100	63	0.63
2	2	5	2500	100	78	0.78
3	2	10	500	100	88	0.88
4	2	10	2500	100	97	0.97
5	2	20	500	100	96	0.96
6	2	20	2500	100	100	1.00
7	5	5	500	100	87	0.87
8	5	5	2500	100	99	0.99
9	5	10	500	100	95	0.95
10	5	10	2500	100	97	0.97
11	5	20	500	100	98	0.98
12	5	20	2500	100	99	0.99
13	3	5	500	100	89	0.89
14	3	5	2500	100	100	1.00
15	3	10	500	100	100	1.00
16	3	10	2500	100	100	1.00
17	3	20	500	100	100	1.00
18	3	20	2500	100	99	0.99
19	7	5	500	100	81	0.81
20	7	5	2500	50	43	0.86
21	7	10	500	50	46	0.92
22	7	10	2500	50	49	0.98
23	7	20	500	50	49	0.98
24	7	20	2500	38	38	1.00

# visualize Rhat values
conv_grp <- conv %>%
  select(condition_lbs, iter, N_cat, N_items, N, Rhat_paragrp, converge_paragrp) %>%
  distinct()

Adding missing grouping variables: `condition`, `parameter_group`

ggplot() +
  geom_violin(data=conv, aes(x=condition_lbs , y=Rhat, group=condition))+
  geom_jitter(data=conv_grp, aes(x=condition_lbs , y=Rhat_paragrp), color="red", alpha=0.75)+
  geom_abline(intercept = 1.10, slope=0, linetype="dashed")+
  coord_flip()+
  labs(
    title=paste0("Estimates of Rhat for ", param, " posteriors" ),
    subtitle ="Plot includes Rhat for each parameter estimate (violin plot) and\n average Rhat of all similar parameters (e.g., all loadings)",
    caption = "Note. Dashed line represent Rhat = 1.10 for a 'converged' posterior"
  ) +
  theme_bw()+
  theme(
    panel.grid = element_blank()
  )

Effect of Simulated Conditions

Factor Loadings (\(\lambda\))

conv_para_grp <- mydata %>%
  filter(parameter_group == "lambda") %>%
  select(all_of(keep_cols)) %>%
  distinct()

## ANOVA on Rhat values
anova_assumptions_check(
  dat = conv_para_grp, outcome = 'Rhat_paragrp',
  factors = c('N_cat', 'N_items', 'N'),
  model = as.formula('Rhat_paragrp ~ N_cat*N_items*N'))


 ============================= 

 Tests and Plots of Normality:


 Shapiro-Wilks Test of Normality of Residuals:

    Shapiro-Wilk normality test

data:  res
W = 0.8, p-value <0.0000000000000002


 K-S Test for Normality of Residuals:

Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test


    One-sample Kolmogorov-Smirnov test

data:  aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


 ============================= 

 Tests of Homogeneity of Variance

 
 Levenes Test:  N_cat 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    3    79.9 <0.0000000000000002 ***
      2134                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N_items 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    2     241 <0.0000000000000002 ***
      2135                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value Pr(>F)   
group    1    10.3 0.0014 **
      2136                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

fit <- summary(aov(Rhat_paragrp ~ N_cat*N_items*N, data=conv_para_grp))
fit

                  Df Sum Sq Mean Sq F value               Pr(>F)    
N_cat              3  0.375  0.1249  269.23 < 0.0000000000000002 ***
N_items            2  0.440  0.2202  474.59 < 0.0000000000000002 ***
N                  1  0.042  0.0416   89.65 < 0.0000000000000002 ***
N_cat:N_items      6  0.107  0.0179   38.48 < 0.0000000000000002 ***
N_cat:N            3  0.005  0.0015    3.31                0.019 *  
N_items:N          2  0.003  0.0015    3.15                0.043 *  
N_cat:N_items:N    6  0.027  0.0045    9.75        0.00000000013 ***
Residuals       2114  0.981  0.0005                                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est)

                omega^2 partial-omega^2 eta_est
N_cat            0.1886          0.2735 0.18933
N_items          0.2220          0.3070 0.22249
N                0.0208          0.0398 0.02101
N_cat:N_items    0.0527          0.0952 0.05412
N_cat:N          0.0016          0.0032 0.00232
N_items:N        0.0010          0.0020 0.00148
N_cat:N_items:N  0.0123          0.0240 0.01371

saved_omega[1,] <- omega2(fit)
saved_eta[1,] <- eta_est

Item Thresholds (\(\tau\))

conv_para_grp <- mydata %>%
  filter(parameter_group == "tau") %>%
  select(all_of(keep_cols)) %>%
  distinct()

## ANOVA on Rhat values
anova_assumptions_check(
  dat = conv_para_grp, outcome = 'Rhat_paragrp',
  factors = c('N_cat', 'N_items', 'N'),
  model = as.formula('Rhat_paragrp ~ N_cat*N_items*N'))


 ============================= 

 Tests and Plots of Normality:


 Shapiro-Wilks Test of Normality of Residuals:

    Shapiro-Wilk normality test

data:  res
W = 0.7, p-value <0.0000000000000002


 K-S Test for Normality of Residuals:

Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test


    One-sample Kolmogorov-Smirnov test

data:  aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


 ============================= 

 Tests of Homogeneity of Variance

 
 Levenes Test:  N_cat 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    3    32.3 <0.0000000000000002 ***
      2134                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N_items 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    2    93.2 <0.0000000000000002 ***
      2135                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    1      76 <0.0000000000000002 ***
      2136                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

fit <- summary(aov(Rhat_paragrp ~ N_cat*N_items*N, data=conv_para_grp))
fit

                  Df Sum Sq Mean Sq F value              Pr(>F)    
N_cat              3 0.0547 0.01824  319.94 <0.0000000000000002 ***
N_items            2 0.0237 0.01183  207.48 <0.0000000000000002 ***
N                  1 0.0146 0.01459  255.89 <0.0000000000000002 ***
N_cat:N_items      6 0.0062 0.00103   18.05 <0.0000000000000002 ***
N_cat:N            3 0.0008 0.00026    4.62              0.0032 ** 
N_items:N          2 0.0047 0.00233   40.90 <0.0000000000000002 ***
N_cat:N_items:N    6 0.0004 0.00006    1.10              0.3580    
Residuals       2114 0.1205 0.00006                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est)

                omega^2 partial-omega^2 eta_est
N_cat            0.2419          0.3092 0.24267
N_items          0.1044          0.1619 0.10492
N                0.0644          0.1065 0.06470
N_cat:N_items    0.0259          0.0457 0.02738
N_cat:N          0.0027          0.0050 0.00350
N_items:N        0.0202          0.0360 0.02068
N_cat:N_items:N  0.0002          0.0003 0.00167

saved_omega[2,] <- omega2(fit)
saved_eta[2,] <- eta_est

Latent Response Variance (\(\theta\))

conv_para_grp <- mydata %>%
  filter(parameter_group == "theta") %>%
  select(all_of(keep_cols)) %>%
  distinct()

## ANOVA on Rhat values
anova_assumptions_check(
  dat = conv_para_grp, outcome = 'Rhat_paragrp',
  factors = c('N_cat', 'N_items', 'N'),
  model = as.formula('Rhat_paragrp ~ N_cat*N_items*N'))


 ============================= 

 Tests and Plots of Normality:


 Shapiro-Wilks Test of Normality of Residuals:

    Shapiro-Wilk normality test

data:  res
W = 0.8, p-value <0.0000000000000002


 K-S Test for Normality of Residuals:

Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test


    One-sample Kolmogorov-Smirnov test

data:  aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


 ============================= 

 Tests of Homogeneity of Variance

 
 Levenes Test:  N_cat 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    3     124 <0.0000000000000002 ***
      2134                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N_items 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    2     258 <0.0000000000000002 ***
      2135                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value           Pr(>F)    
group    1    54.8 0.00000000000019 ***
      2136                             
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

fit <- summary(aov(Rhat_paragrp ~ N_cat*N_items*N, data=conv_para_grp))
fit

                  Df Sum Sq Mean Sq F value               Pr(>F)    
N_cat              3  0.614   0.205  288.25 < 0.0000000000000002 ***
N_items            2  0.741   0.371  522.07 < 0.0000000000000002 ***
N                  1  0.138   0.138  194.78 < 0.0000000000000002 ***
N_cat:N_items      6  0.254   0.042   59.55 < 0.0000000000000002 ***
N_cat:N            3  0.006   0.002    2.96                0.031 *  
N_items:N          2  0.032   0.016   22.37        0.00000000024 ***
N_cat:N_items:N    6  0.008   0.001    1.88                0.080 .  
Residuals       2114  1.501   0.001                                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est)

                omega^2 partial-omega^2 eta_est
N_cat            0.1857          0.2873 0.18637
N_items          0.2246          0.3277 0.22504
N                0.0418          0.0831 0.04198
N_cat:N_items    0.0757          0.1411 0.07700
N_cat:N          0.0013          0.0027 0.00192
N_items:N        0.0092          0.0196 0.00964
N_cat:N_items:N  0.0011          0.0025 0.00243

saved_omega[3,] <- omega2(fit)
saved_eta[3,] <- eta_est

Response Time Intercepts (\(\beta_{lrt}\))

conv_para_grp <- mydata %>%
  filter(parameter_group == "beta_lrt") %>%
  select(all_of(keep_cols)) %>%
  distinct()

## ANOVA on Rhat values
anova_assumptions_check(
  dat = conv_para_grp, outcome = 'Rhat_paragrp',
  factors = c('N_cat', 'N_items', 'N'),
  model = as.formula('Rhat_paragrp ~ N_cat*N_items*N'))


 ============================= 

 Tests and Plots of Normality:


 Shapiro-Wilks Test of Normality of Residuals:

    Shapiro-Wilk normality test

data:  res
W = 0.8, p-value <0.0000000000000002


 K-S Test for Normality of Residuals:

Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test


    One-sample Kolmogorov-Smirnov test

data:  aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


 ============================= 

 Tests of Homogeneity of Variance

 
 Levenes Test:  N_cat 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    3    86.4 <0.0000000000000002 ***
      2134                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N_items 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    2     233 <0.0000000000000002 ***
      2135                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value Pr(>F)   
group    1    8.15 0.0043 **
      2136                  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

fit <- summary(aov(Rhat_paragrp ~ N_cat*N_items*N, data=conv_para_grp))
fit

                  Df Sum Sq Mean Sq F value              Pr(>F)    
N_cat              3  0.168  0.0560  163.03 <0.0000000000000002 ***
N_items            2  0.261  0.1303  379.56 <0.0000000000000002 ***
N                  1  0.002  0.0018    5.35               0.021 *  
N_cat:N_items      6  0.068  0.0113   32.80 <0.0000000000000002 ***
N_cat:N            3  0.001  0.0004    1.04               0.375    
N_items:N          2  0.001  0.0007    1.94               0.145    
N_cat:N_items:N    6  0.003  0.0006    1.69               0.118    
Residuals       2114  0.726  0.0003                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est)

                omega^2 partial-omega^2  eta_est
N_cat            0.1357          0.1852 0.136558
N_items          0.2113          0.2615 0.211958
N                0.0012          0.0020 0.001493
N_cat:N_items    0.0533          0.0819 0.054942
N_cat:N          0.0000          0.0001 0.000868
N_items:N        0.0005          0.0009 0.001081
N_cat:N_items:N  0.0012          0.0019 0.002839

saved_omega[4,] <- omega2(fit)
saved_eta[4,] <- eta_est

Response Time Precision (\(\sigma_{lrt}\))

conv_para_grp <- mydata %>%
  filter(parameter_group == "sigma_lrt") %>%
  select(all_of(keep_cols)) %>%
  distinct()

## ANOVA on Rhat values
anova_assumptions_check(
  dat = conv_para_grp, outcome = 'Rhat_paragrp',
  factors = c('N_cat', 'N_items', 'N'),
  model = as.formula('Rhat_paragrp ~ N_cat*N_items*N'))


 ============================= 

 Tests and Plots of Normality:


 Shapiro-Wilks Test of Normality of Residuals:

    Shapiro-Wilk normality test

data:  res
W = 0.5, p-value <0.0000000000000002


 K-S Test for Normality of Residuals:

Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test


    One-sample Kolmogorov-Smirnov test

data:  aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


 ============================= 

 Tests of Homogeneity of Variance

 
 Levenes Test:  N_cat 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    3     202 <0.0000000000000002 ***
      2134                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N_items 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    2     285 <0.0000000000000002 ***
      2135                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    1      80 <0.0000000000000002 ***
      2136                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

fit <- summary(aov(Rhat_paragrp ~ N_cat*N_items*N, data=conv_para_grp))
fit

                  Df  Sum Sq  Mean Sq F value               Pr(>F)    
N_cat              3 0.00853 0.002843  231.39 < 0.0000000000000002 ***
N_items            2 0.00628 0.003140  255.63 < 0.0000000000000002 ***
N                  1 0.00103 0.001026   83.53 < 0.0000000000000002 ***
N_cat:N_items      6 0.00674 0.001123   91.39 < 0.0000000000000002 ***
N_cat:N            3 0.00089 0.000296   24.07   0.0000000000000026 ***
N_items:N          2 0.00086 0.000431   35.04   0.0000000000000011 ***
N_cat:N_items:N    6 0.00034 0.000056    4.55              0.00014 ***
Residuals       2114 0.02597 0.000012                                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est)

                omega^2 partial-omega^2 eta_est
N_cat            0.1677          0.2443 0.16845
N_items          0.1235          0.1924 0.12406
N                0.0200          0.0372 0.02027
N_cat:N_items    0.1316          0.2023 0.13306
N_cat:N          0.0168          0.0314 0.01752
N_items:N        0.0165          0.0309 0.01701
N_cat:N_items:N  0.0052          0.0099 0.00662

saved_omega[5,] <- omega2(fit)
saved_eta[5,] <- eta_est

Response Time Factor Precision (\(\sigma_s\))

conv_para_grp <- mydata %>%
  filter(parameter_group == "sigma_s") %>%
  select(all_of(keep_cols)) %>%
  distinct()

## ANOVA on Rhat values
anova_assumptions_check(
  dat = conv_para_grp, outcome = 'Rhat_paragrp',
  factors = c('N_cat', 'N_items', 'N'),
  model = as.formula('Rhat_paragrp ~ N_cat*N_items*N'))


 ============================= 

 Tests and Plots of Normality:


 Shapiro-Wilks Test of Normality of Residuals:

    Shapiro-Wilk normality test

data:  res
W = 0.8, p-value <0.0000000000000002


 K-S Test for Normality of Residuals:

Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test


    One-sample Kolmogorov-Smirnov test

data:  aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


 ============================= 

 Tests of Homogeneity of Variance

 
 Levenes Test:  N_cat 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    3    34.7 <0.0000000000000002 ***
      2134                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N_items 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    2     190 <0.0000000000000002 ***
      2135                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value Pr(>F)
group    1    0.03   0.86
      2136

fit <- summary(aov(Rhat_paragrp ~ N_cat*N_items*N, data=conv_para_grp))
fit

                  Df Sum Sq Mean Sq F value              Pr(>F)    
N_cat              3 0.0167 0.00555   66.57 <0.0000000000000002 ***
N_items            2 0.0408 0.02039  244.42 <0.0000000000000002 ***
N                  1 0.0000 0.00003    0.31                0.58    
N_cat:N_items      6 0.0080 0.00134   16.03 <0.0000000000000002 ***
N_cat:N            3 0.0001 0.00004    0.44                0.73    
N_items:N          2 0.0005 0.00023    2.82                0.06 .  
N_cat:N_items:N    6 0.0003 0.00005    0.60                0.73    
Residuals       2114 0.1763 0.00008                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est)

                omega^2 partial-omega^2  eta_est
N_cat            0.0676          0.0843 0.068641
N_items          0.1673          0.1855 0.168011
N               -0.0002         -0.0003 0.000106
N_cat:N_items    0.0310          0.0405 0.033056
N_cat:N         -0.0006         -0.0008 0.000452
N_items:N        0.0012          0.0017 0.001935
N_cat:N_items:N -0.0008         -0.0011 0.001236

saved_omega[6,] <- omega2(fit)
saved_eta[6,] <- eta_est

Factor Covariance (\(\sigma_{st}\))

conv_para_grp <- mydata %>%
  filter(parameter_group == "sigma_st") %>%
  select(all_of(keep_cols)) %>%
  distinct()

## ANOVA on Rhat values
anova_assumptions_check(
  dat = conv_para_grp, outcome = 'Rhat_paragrp',
  factors = c('N_cat', 'N_items', 'N'),
  model = as.formula('Rhat_paragrp ~ N_cat*N_items*N'))


 ============================= 

 Tests and Plots of Normality:


 Shapiro-Wilks Test of Normality of Residuals:

    Shapiro-Wilk normality test

data:  res
W = 0.7, p-value <0.0000000000000002


 K-S Test for Normality of Residuals:

Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test


    One-sample Kolmogorov-Smirnov test

data:  aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


 ============================= 

 Tests of Homogeneity of Variance

 
 Levenes Test:  N_cat 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    3    58.9 <0.0000000000000002 ***
      2134                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N_items 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    2    94.5 <0.0000000000000002 ***
      2135                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value     Pr(>F)    
group    1    24.4 0.00000085 ***
      2136                       
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

fit <- summary(aov(Rhat_paragrp ~ N_cat*N_items*N, data=conv_para_grp))
fit

                  Df Sum Sq Mean Sq F value               Pr(>F)    
N_cat              3  0.054  0.0180   82.10 < 0.0000000000000002 ***
N_items            2  0.071  0.0353  160.59 < 0.0000000000000002 ***
N                  1  0.005  0.0046   20.84      0.0000052682224 ***
N_cat:N_items      6  0.015  0.0025   11.28      0.0000000000019 ***
N_cat:N            3  0.002  0.0005    2.47                 0.06 .  
N_items:N          2  0.001  0.0003    1.29                 0.28    
N_cat:N_items:N    6  0.001  0.0001    0.49                 0.81    
Residuals       2114  0.464  0.0002                                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est)

                omega^2 partial-omega^2  eta_est
N_cat            0.0874          0.1022 0.088504
N_items          0.1146          0.1299 0.115409
N                0.0071          0.0092 0.007490
N_cat:N_items    0.0222          0.0280 0.024326
N_cat:N          0.0016          0.0021 0.002668
N_items:N        0.0002          0.0003 0.000927
N_cat:N_items:N -0.0011         -0.0014 0.001065

saved_omega[7,] <- omega2(fit)
saved_eta[7,] <- eta_est

PID Relationship (\(\rho\))

conv_para_grp <- mydata %>%
  filter(parameter_group == "rho") %>%
  select(all_of(keep_cols)) %>%
  distinct()

## ANOVA on Rhat values
anova_assumptions_check(
  dat = conv_para_grp, outcome = 'Rhat_paragrp',
  factors = c('N_cat', 'N_items', 'N'),
  model = as.formula('Rhat_paragrp ~ N_cat*N_items*N'))


 ============================= 

 Tests and Plots of Normality:


 Shapiro-Wilks Test of Normality of Residuals:

    Shapiro-Wilk normality test

data:  res
W = 0.8, p-value <0.0000000000000002


 K-S Test for Normality of Residuals:

Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test


    One-sample Kolmogorov-Smirnov test

data:  aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


 ============================= 

 Tests of Homogeneity of Variance

 
 Levenes Test:  N_cat 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    3    45.5 <0.0000000000000002 ***
      2134                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N_items 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    2      74 <0.0000000000000002 ***
      2135                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value   Pr(>F)    
group    1    19.3 0.000012 ***
      2136                     
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

fit <- summary(aov(Rhat_paragrp ~ N_cat*N_items*N, data=conv_para_grp))
fit

                  Df Sum Sq Mean Sq F value               Pr(>F)    
N_cat              3  0.162  0.0540   45.25 < 0.0000000000000002 ***
N_items            2  0.185  0.0925   77.44 < 0.0000000000000002 ***
N                  1  0.027  0.0273   22.88          0.000001846 ***
N_cat:N_items      6  0.053  0.0089    7.44          0.000000067 ***
N_cat:N            3  0.007  0.0024    1.99                0.114    
N_items:N          2  0.008  0.0039    3.24                0.039 *  
N_cat:N_items:N    6  0.010  0.0016    1.34                0.237    
Residuals       2114  2.524  0.0012                                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est)

                omega^2 partial-omega^2 eta_est
N_cat            0.0532          0.0585 0.05447
N_items          0.0613          0.0667 0.06213
N                0.0088          0.0101 0.00918
N_cat:N_items    0.0155          0.0178 0.01791
N_cat:N          0.0012          0.0014 0.00239
N_items:N        0.0018          0.0021 0.00260
N_cat:N_items:N  0.0008          0.0009 0.00322

saved_omega[8,] <- omega2(fit)
saved_eta[8,] <- eta_est

Factor Reliability (\(\omega\))

conv_para_grp <- mydata %>%
  filter(parameter_group == "omega") %>%
  select(all_of(keep_cols)) %>%
  distinct()

## ANOVA on Rhat values
anova_assumptions_check(
  dat = conv_para_grp, outcome = 'Rhat_paragrp',
  factors = c('N_cat', 'N_items', 'N'),
  model = as.formula('Rhat_paragrp ~ N_cat*N_items*N'))


 ============================= 

 Tests and Plots of Normality:


 Shapiro-Wilks Test of Normality of Residuals:

    Shapiro-Wilk normality test

data:  res
W = 0.8, p-value <0.0000000000000002


 K-S Test for Normality of Residuals:

Warning in ks.test(aov.out$residuals, "pnorm", alternative = "two.sided"): ties
should not be present for the Kolmogorov-Smirnov test


    One-sample Kolmogorov-Smirnov test

data:  aov.out$residuals
D = 0.5, p-value <0.0000000000000002
alternative hypothesis: two-sided

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.

`stat_bin()` using `bins = 30`. Pick better value with `binwidth`.


 ============================= 

 Tests of Homogeneity of Variance

 
 Levenes Test:  N_cat 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    3    67.1 <0.0000000000000002 ***
      2134                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N_items 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value              Pr(>F)    
group    2     124 <0.0000000000000002 ***
      2135                                
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

 
 Levenes Test:  N 
 
 
Levene's Test for Homogeneity of Variance (center = "mean")
        Df F value           Pr(>F)    
group    1    55.7 0.00000000000012 ***
      2136                             
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

fit <- summary(aov(Rhat_paragrp ~ N_cat*N_items*N, data=conv_para_grp))
fit

                  Df Sum Sq Mean Sq F value               Pr(>F)    
N_cat              3  0.311  0.1036   80.46 < 0.0000000000000002 ***
N_items            2  0.381  0.1904  147.84 < 0.0000000000000002 ***
N                  1  0.087  0.0874   67.85  0.00000000000000031 ***
N_cat:N_items      6  0.124  0.0206   16.01 < 0.0000000000000002 ***
N_cat:N            3  0.007  0.0024    1.89              0.12980    
N_items:N          2  0.023  0.0113    8.78              0.00016 ***
N_cat:N_items:N    6  0.005  0.0008    0.58              0.74283    
Residuals       2114  2.723  0.0013                                 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

eta_est <- (fit[[1]]$`Sum Sq`/sum(fit[[1]]$`Sum Sq`))[1:7]
cbind(omega2(fit),p_omega2(fit), eta_est)

                omega^2 partial-omega^2 eta_est
N_cat            0.0839          0.1003 0.08494
N_items          0.1033          0.1208 0.10405
N                0.0235          0.0303 0.02387
N_cat:N_items    0.0317          0.0404 0.03380
N_cat:N          0.0009          0.0012 0.00199
N_items:N        0.0055          0.0072 0.00618
N_cat:N_items:N -0.0009         -0.0012 0.00123

saved_omega[9,] <- omega2(fit)
saved_eta[9,] <- eta_est

Manuscript Tables and Figures (latex formated)

Tables

print(
  xtable(
    t(saved_omega)
    , caption = c("Effect of design factors on relative bias estimates: omega2")
    ,align = "lrrrrrrrrr", digits = 3
  ),
  include.rownames=T,
  booktabs=T
)

% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Sun Feb 13 14:28:59 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrr}
  \toprule
 & lambda & tau & theta & beta\_lrt & sigma\_lrt & sigma\_s & sigma\_ts & rho & omega \\ 
  \midrule
N\_cat & 0.189 & 0.242 & 0.186 & 0.136 & 0.168 & 0.068 & 0.087 & 0.053 & 0.084 \\ 
  N\_items & 0.222 & 0.104 & 0.225 & 0.211 & 0.123 & 0.167 & 0.115 & 0.061 & 0.103 \\ 
  N & 0.021 & 0.064 & 0.042 & 0.001 & 0.020 & -0.000 & 0.007 & 0.009 & 0.024 \\ 
  N\_cat:N\_items & 0.053 & 0.026 & 0.076 & 0.053 & 0.132 & 0.031 & 0.022 & 0.015 & 0.032 \\ 
  N\_cat:N & 0.002 & 0.003 & 0.001 & 0.000 & 0.017 & -0.001 & 0.002 & 0.001 & 0.001 \\ 
  N\_items:N & 0.001 & 0.020 & 0.009 & 0.000 & 0.016 & 0.001 & 0.000 & 0.002 & 0.005 \\ 
  N\_cat:N\_items:N & 0.012 & 0.000 & 0.001 & 0.001 & 0.005 & -0.001 & -0.001 & 0.001 & -0.001 \\ 
   \bottomrule
\end{tabular}
\caption{Effect of design factors on relative bias estimates: omega2} 
\end{table}

print(
  xtable(
    t(saved_eta)
    , caption = c("Effect of design factors on relative bias estimates: eta2")
    ,align = "lrrrrrrrrr", digits = 3
  ),
  include.rownames=T,
  booktabs=T
)

% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Sun Feb 13 14:28:59 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrr}
  \toprule
 & lambda & tau & theta & beta\_lrt & sigma\_lrt & sigma\_s & sigma\_ts & rho & omega \\ 
  \midrule
N\_cat & 0.189 & 0.243 & 0.186 & 0.137 & 0.168 & 0.069 & 0.089 & 0.054 & 0.085 \\ 
  N\_items & 0.222 & 0.105 & 0.225 & 0.212 & 0.124 & 0.168 & 0.115 & 0.062 & 0.104 \\ 
  N & 0.021 & 0.065 & 0.042 & 0.001 & 0.020 & 0.000 & 0.007 & 0.009 & 0.024 \\ 
  N\_cat:N\_items & 0.054 & 0.027 & 0.077 & 0.055 & 0.133 & 0.033 & 0.024 & 0.018 & 0.034 \\ 
  N\_cat:N & 0.002 & 0.004 & 0.002 & 0.001 & 0.018 & 0.000 & 0.003 & 0.002 & 0.002 \\ 
  N\_items:N & 0.001 & 0.021 & 0.010 & 0.001 & 0.017 & 0.002 & 0.001 & 0.003 & 0.006 \\ 
  N\_cat:N\_items:N & 0.014 & 0.002 & 0.002 & 0.003 & 0.007 & 0.001 & 0.001 & 0.003 & 0.001 \\ 
   \bottomrule
\end{tabular}
\caption{Effect of design factors on relative bias estimates: eta2} 
\end{table}

keep_cols <- c("condition", "iter", "N", "N_items", "N_cat", "parameter_group", "Rhat_paragrp", "converge_paragrp", "converge_proportion_paragrp")

tbl_dat <- mydata %>%
  select(all_of(keep_cols)) %>%
  filter(
    !is.na(parameter_group)
    , parameter_group != "lambda (STD)"
  ) %>%
  distinct() %>%
  mutate(
    prop_con = ifelse(converge_proportion_paragrp > 0.5, ">50% Converged", "<=50% Converged")
  )


# get average Rhat and SD for each condition and parameter group
sum_tab <- tbl_dat %>%
  group_by(N_cat, N_items, N, parameter_group) %>%
  summarise(
    AvgRhat = mean(Rhat_paragrp),
    SDRhat = sd(Rhat_paragrp),
    AvgPropConv = mean(converge_proportion_paragrp)
  )

`summarise()` has grouped output by 'N_cat', 'N_items', 'N'. You can override using the `.groups` argument.

# table 1: 2 category data
T1 <- sum_tab %>%
  filter(N_cat == 2) %>%
  pivot_wider(
    id_cols = c("parameter_group", "N")
    , names_from = "N_items"
    , values_from = all_of(c("AvgRhat", "SDRhat", "AvgPropConv"))
  ) %>%
  arrange(.,parameter_group)
# reordering of rows to more logical for presentation
T1 <- T1[c(3:4, 15:18, 1:2, 5:8, 13:14, 11:12, 9:10) ,]
print(
  xtable(
    T1
    , caption = c("Posterior convergence by Rhat summary: Dichotomous items")
    ,align = "llrrrrrrrrrr"
  ),
  include.rownames=F,
  booktabs=T
)

% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Sun Feb 13 14:29:00 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrrr}
  \toprule
parameter\_group & N & AvgRhat\_5 & AvgRhat\_10 & AvgRhat\_20 & SDRhat\_5 & SDRhat\_10 & SDRhat\_20 & AvgPropConv\_5 & AvgPropConv\_10 & AvgPropConv\_20 \\ 
  \midrule
lambda & 500 & 1.09 & 1.06 & 1.04 & 0.05 & 0.02 & 0.01 & 0.68 & 0.85 & 0.95 \\ 
  lambda & 2500 & 1.10 & 1.05 & 1.03 & 0.05 & 0.01 & 0.00 & 0.65 & 0.90 & 0.97 \\ 
  tau & 500 & 1.03 & 1.02 & 1.01 & 0.02 & 0.01 & 0.00 & 0.96 & 0.98 & 1.00 \\ 
  tau & 2500 & 1.02 & 1.01 & 1.01 & 0.01 & 0.00 & 0.00 & 0.98 & 1.00 & 1.00 \\ 
  theta & 500 & 1.14 & 1.08 & 1.05 & 0.07 & 0.03 & 0.01 & 0.50 & 0.76 & 0.92 \\ 
  theta & 2500 & 1.11 & 1.05 & 1.03 & 0.05 & 0.01 & 0.01 & 0.62 & 0.89 & 0.97 \\ 
  beta\_lrt & 500 & 1.07 & 1.04 & 1.02 & 0.04 & 0.02 & 0.01 & 0.80 & 0.93 & 0.99 \\ 
  beta\_lrt & 2500 & 1.07 & 1.03 & 1.02 & 0.04 & 0.01 & 0.01 & 0.80 & 0.97 & 1.00 \\ 
  sigma\_lrt & 500 & 1.01 & 1.00 & 1.00 & 0.01 & 0.01 & 0.00 & 0.97 & 1.00 & 1.00 \\ 
  sigma\_lrt & 2500 & 1.01 & 1.00 & 1.00 & 0.01 & 0.00 & 0.00 & 0.99 & 1.00 & 1.00 \\ 
  sigma\_s & 500 & 1.02 & 1.01 & 1.00 & 0.02 & 0.01 & 0.00 & 0.99 & 1.00 & 1.00 \\ 
  sigma\_s & 2500 & 1.02 & 1.01 & 1.00 & 0.02 & 0.01 & 0.00 & 0.97 & 1.00 & 1.00 \\ 
  sigma\_st & 500 & 1.04 & 1.02 & 1.01 & 0.04 & 0.02 & 0.01 & 0.95 & 1.00 & 1.00 \\ 
  sigma\_st & 2500 & 1.03 & 1.02 & 1.01 & 0.03 & 0.01 & 0.01 & 0.98 & 1.00 & 1.00 \\ 
  rho & 500 & 1.07 & 1.06 & 1.04 & 0.08 & 0.05 & 0.02 & 0.82 & 0.85 & 0.97 \\ 
  rho & 2500 & 1.07 & 1.03 & 1.02 & 0.07 & 0.03 & 0.01 & 0.80 & 0.97 & 1.00 \\ 
  omega & 500 & 1.10 & 1.05 & 1.03 & 0.07 & 0.04 & 0.03 & 0.63 & 0.88 & 0.96 \\ 
  omega & 2500 & 1.08 & 1.03 & 1.02 & 0.08 & 0.02 & 0.02 & 0.78 & 0.97 & 1.00 \\ 
   \bottomrule
\end{tabular}
\caption{Posterior convergence by Rhat summary: Dichotomous items} 
\end{table}

# table 2: 5 category data
T2 <- sum_tab %>%
  filter(N_cat == 5) %>%
  pivot_wider(
    id_cols = c("parameter_group", "N")
    , names_from = "N_items"
    , values_from = all_of(c("AvgRhat", "SDRhat", "AvgPropConv"))
  ) %>%
  arrange(.,parameter_group)
# reordering of rows to more logical for presentation
T2 <- T2[c(3:4, 15:18, 1:2, 5:8, 13:14, 11:12, 9:10) ,]
print(
  xtable(
    T2
    , caption = c("Posterior convergence by Rhat summary: Five category items")
    ,align = "llrrrrrrrrrr"
  ),
  include.rownames=F,
  booktabs=T
)

% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Sun Feb 13 14:29:00 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrrr}
  \toprule
parameter\_group & N & AvgRhat\_5 & AvgRhat\_10 & AvgRhat\_20 & SDRhat\_5 & SDRhat\_10 & SDRhat\_20 & AvgPropConv\_5 & AvgPropConv\_10 & AvgPropConv\_20 \\ 
  \midrule
lambda & 500 & 1.07 & 1.04 & 1.04 & 0.03 & 0.01 & 0.01 & 0.78 & 0.92 & 0.94 \\ 
  lambda & 2500 & 1.04 & 1.03 & 1.03 & 0.02 & 0.01 & 0.01 & 0.91 & 0.96 & 0.97 \\ 
  tau & 500 & 1.02 & 1.02 & 1.02 & 0.01 & 0.00 & 0.00 & 0.97 & 0.99 & 1.00 \\ 
  tau & 2500 & 1.02 & 1.02 & 1.02 & 0.01 & 0.00 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  theta & 500 & 1.08 & 1.05 & 1.04 & 0.04 & 0.01 & 0.01 & 0.73 & 0.91 & 0.94 \\ 
  theta & 2500 & 1.05 & 1.03 & 1.03 & 0.02 & 0.01 & 0.01 & 0.90 & 0.96 & 0.97 \\ 
  beta\_lrt & 500 & 1.03 & 1.02 & 1.01 & 0.02 & 0.02 & 0.01 & 0.93 & 0.98 & 1.00 \\ 
  beta\_lrt & 2500 & 1.03 & 1.02 & 1.01 & 0.02 & 0.01 & 0.01 & 0.98 & 1.00 & 1.00 \\ 
  sigma\_lrt & 500 & 1.00 & 1.00 & 1.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_lrt & 2500 & 1.00 & 1.00 & 1.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_s & 500 & 1.01 & 1.00 & 1.00 & 0.01 & 0.01 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_s & 2500 & 1.01 & 1.00 & 1.00 & 0.01 & 0.01 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_st & 500 & 1.02 & 1.01 & 1.01 & 0.02 & 0.01 & 0.01 & 0.98 & 1.00 & 1.00 \\ 
  sigma\_st & 2500 & 1.02 & 1.01 & 1.01 & 0.01 & 0.01 & 0.01 & 1.00 & 1.00 & 1.00 \\ 
  rho & 500 & 1.04 & 1.03 & 1.03 & 0.04 & 0.03 & 0.02 & 0.91 & 0.94 & 0.98 \\ 
  rho & 2500 & 1.03 & 1.02 & 1.02 & 0.03 & 0.02 & 0.02 & 0.97 & 1.00 & 1.00 \\ 
  omega & 500 & 1.05 & 1.04 & 1.03 & 0.04 & 0.03 & 0.03 & 0.87 & 0.95 & 0.98 \\ 
  omega & 2500 & 1.03 & 1.03 & 1.02 & 0.03 & 0.02 & 0.02 & 0.99 & 0.97 & 0.99 \\ 
   \bottomrule
\end{tabular}
\caption{Posterior convergence by Rhat summary: Five category items} 
\end{table}

# table 3: 3 category data
T3 <- sum_tab %>%
  filter(N_cat == 3) %>%
  pivot_wider(
    id_cols = c("parameter_group", "N")
    , names_from = "N_items"
    , values_from = all_of(c("AvgRhat", "SDRhat", "AvgPropConv"))
  ) %>%
  arrange(.,parameter_group)
# reordering of rows to more logical for presentation
T3 <- T3[c(3:4, 15:18, 1:2, 5:8, 13:14, 11:12, 9:10) ,]
print(
  xtable(
    T3
    , caption = c("Posterior convergence by Rhat summary: Three category items")
    ,align = "llrrrrrrrrrr"
  ),
  include.rownames=F,
  booktabs=T
)

% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Sun Feb 13 14:29:00 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrrr}
  \toprule
parameter\_group & N & AvgRhat\_5 & AvgRhat\_10 & AvgRhat\_20 & SDRhat\_5 & SDRhat\_10 & SDRhat\_20 & AvgPropConv\_5 & AvgPropConv\_10 & AvgPropConv\_20 \\ 
  \midrule
lambda & 500 & 1.06 & 1.03 & 1.02 & 0.03 & 0.01 & 0.00 & 0.87 & 0.98 & 0.99 \\ 
  lambda & 2500 & 1.04 & 1.02 & 1.02 & 0.01 & 0.01 & 0.00 & 0.95 & 0.99 & 1.00 \\ 
  tau & 500 & 1.02 & 1.01 & 1.01 & 0.01 & 0.00 & 0.00 & 0.98 & 1.00 & 1.00 \\ 
  tau & 2500 & 1.01 & 1.01 & 1.01 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  theta & 500 & 1.07 & 1.03 & 1.02 & 0.04 & 0.01 & 0.00 & 0.80 & 0.98 & 0.99 \\ 
  theta & 2500 & 1.04 & 1.02 & 1.02 & 0.02 & 0.01 & 0.00 & 0.93 & 0.99 & 1.00 \\ 
  beta\_lrt & 500 & 1.03 & 1.02 & 1.01 & 0.02 & 0.01 & 0.01 & 0.96 & 1.00 & 1.00 \\ 
  beta\_lrt & 2500 & 1.03 & 1.02 & 1.01 & 0.02 & 0.01 & 0.01 & 0.99 & 1.00 & 1.00 \\ 
  sigma\_lrt & 500 & 1.00 & 1.00 & 1.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_lrt & 2500 & 1.00 & 1.00 & 1.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_s & 500 & 1.01 & 1.00 & 1.00 & 0.01 & 0.01 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_s & 2500 & 1.01 & 1.00 & 1.00 & 0.01 & 0.01 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_st & 500 & 1.01 & 1.01 & 1.01 & 0.01 & 0.01 & 0.01 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_st & 2500 & 1.01 & 1.01 & 1.00 & 0.01 & 0.01 & 0.01 & 1.00 & 1.00 & 1.00 \\ 
  rho & 500 & 1.03 & 1.03 & 1.02 & 0.04 & 0.02 & 0.02 & 0.97 & 0.99 & 0.99 \\ 
  rho & 2500 & 1.03 & 1.02 & 1.02 & 0.02 & 0.02 & 0.01 & 0.98 & 1.00 & 1.00 \\ 
  omega & 500 & 1.05 & 1.02 & 1.02 & 0.04 & 0.01 & 0.01 & 0.89 & 1.00 & 1.00 \\ 
  omega & 2500 & 1.02 & 1.02 & 1.01 & 0.02 & 0.01 & 0.02 & 1.00 & 1.00 & 0.99 \\ 
   \bottomrule
\end{tabular}
\caption{Posterior convergence by Rhat summary: Three category items} 
\end{table}

# table 4: 7 category data
T4 <- sum_tab %>%
  filter(N_cat == 7) %>%
  pivot_wider(
    id_cols = c("parameter_group", "N")
    , names_from = "N_items"
    , values_from = all_of(c("AvgRhat", "SDRhat", "AvgPropConv"))
  ) %>%
  arrange(.,parameter_group)
# reordering of rows to more logical for presentation
T4 <- T4[c(3:4, 15:18, 1:2, 5:8, 13:14, 11:12, 9:10) ,]
print(
  xtable(
    T4
    , caption = c("Posterior convergence by Rhat summary: Seven category items")
    ,align = "llrrrrrrrrrr"
  ),
  include.rownames=F,
  booktabs=T
)

% latex table generated in R 4.0.5 by xtable 1.8-4 package
% Sun Feb 13 14:29:00 2022
\begin{table}[ht]
\centering
\begin{tabular}{lrrrrrrrrrr}
  \toprule
parameter\_group & N & AvgRhat\_5 & AvgRhat\_10 & AvgRhat\_20 & SDRhat\_5 & SDRhat\_10 & SDRhat\_20 & AvgPropConv\_5 & AvgPropConv\_10 & AvgPropConv\_20 \\ 
  \midrule
lambda & 500 & 1.07 & 1.05 & 1.05 & 0.03 & 0.02 & 0.01 & 0.78 & 0.85 & 0.88 \\ 
  lambda & 2500 & 1.06 & 1.05 & 1.04 & 0.02 & 0.01 & 0.01 & 0.83 & 0.90 & 0.92 \\ 
  tau & 500 & 1.03 & 1.02 & 1.02 & 0.01 & 0.00 & 0.00 & 0.95 & 0.99 & 0.99 \\ 
  tau & 2500 & 1.02 & 1.02 & 1.02 & 0.01 & 0.00 & 0.00 & 0.99 & 1.00 & 1.00 \\ 
  theta & 500 & 1.08 & 1.06 & 1.05 & 0.03 & 0.02 & 0.01 & 0.75 & 0.84 & 0.86 \\ 
  theta & 2500 & 1.06 & 1.05 & 1.04 & 0.03 & 0.01 & 0.01 & 0.82 & 0.90 & 0.92 \\ 
  beta\_lrt & 500 & 1.03 & 1.02 & 1.01 & 0.02 & 0.01 & 0.01 & 0.96 & 0.99 & 1.00 \\ 
  beta\_lrt & 2500 & 1.03 & 1.02 & 1.01 & 0.02 & 0.01 & 0.01 & 0.95 & 0.99 & 1.00 \\ 
  sigma\_lrt & 500 & 1.00 & 1.00 & 1.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_lrt & 2500 & 1.00 & 1.00 & 1.00 & 0.00 & 0.00 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_s & 500 & 1.01 & 1.00 & 1.00 & 0.01 & 0.01 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_s & 2500 & 1.01 & 1.00 & 1.00 & 0.01 & 0.01 & 0.00 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_st & 500 & 1.02 & 1.01 & 1.01 & 0.02 & 0.01 & 0.01 & 1.00 & 1.00 & 1.00 \\ 
  sigma\_st & 2500 & 1.02 & 1.01 & 1.01 & 0.01 & 0.01 & 0.01 & 1.00 & 1.00 & 1.00 \\ 
  rho & 500 & 1.04 & 1.03 & 1.02 & 0.04 & 0.02 & 0.01 & 0.87 & 0.98 & 1.00 \\ 
  rho & 2500 & 1.04 & 1.02 & 1.02 & 0.03 & 0.02 & 0.01 & 0.90 & 0.98 & 1.00 \\ 
  omega & 500 & 1.07 & 1.04 & 1.03 & 0.06 & 0.03 & 0.03 & 0.81 & 0.92 & 0.98 \\ 
  omega & 2500 & 1.04 & 1.03 & 1.02 & 0.04 & 0.02 & 0.02 & 0.86 & 0.98 & 1.00 \\ 
   \bottomrule
\end{tabular}
\caption{Posterior convergence by Rhat summary: Seven category items} 
\end{table}

sessionInfo()

R version 4.0.5 (2021-03-31)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 10 x64 (build 22000)

Matrix products: default

locale:
[1] LC_COLLATE=English_United States.1252 
[2] LC_CTYPE=English_United States.1252   
[3] LC_MONETARY=English_United States.1252
[4] LC_NUMERIC=C                          
[5] LC_TIME=English_United States.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] car_3.0-10           carData_3.0-4        mvtnorm_1.1-1       
 [4] LaplacesDemon_16.1.4 runjags_2.2.0-2      lme4_1.1-26         
 [7] Matrix_1.3-2         sirt_3.9-4           R2jags_0.6-1        
[10] rjags_4-12           eRm_1.0-2            diffIRT_1.5         
[13] statmod_1.4.35       xtable_1.8-4         kableExtra_1.3.4    
[16] lavaan_0.6-7         polycor_0.7-10       bayesplot_1.8.0     
[19] ggmcmc_1.5.1.1       coda_0.19-4          data.table_1.14.0   
[22] patchwork_1.1.1      forcats_0.5.1        stringr_1.4.0       
[25] dplyr_1.0.5          purrr_0.3.4          readr_1.4.0         
[28] tidyr_1.1.3          tibble_3.1.0         ggplot2_3.3.5       
[31] tidyverse_1.3.0      workflowr_1.6.2     

loaded via a namespace (and not attached):
 [1] minqa_1.2.4        TAM_3.5-19         colorspace_2.0-0   rio_0.5.26        
 [5] ellipsis_0.3.1     ggridges_0.5.3     rprojroot_2.0.2    fs_1.5.0          
 [9] rstudioapi_0.13    farver_2.1.0       fansi_0.4.2        lubridate_1.7.10  
[13] xml2_1.3.2         splines_4.0.5      mnormt_2.0.2       knitr_1.31        
[17] jsonlite_1.7.2     nloptr_1.2.2.2     broom_0.7.5        dbplyr_2.1.0      
[21] compiler_4.0.5     httr_1.4.2         backports_1.2.1    assertthat_0.2.1  
[25] cli_2.3.1          later_1.1.0.1      htmltools_0.5.1.1  tools_4.0.5       
[29] gtable_0.3.0       glue_1.4.2         Rcpp_1.0.7         cellranger_1.1.0  
[33] jquerylib_0.1.3    vctrs_0.3.6        svglite_2.0.0      nlme_3.1-152      
[37] psych_2.0.12       xfun_0.21          ps_1.6.0           openxlsx_4.2.3    
[41] rvest_1.0.0        lifecycle_1.0.0    MASS_7.3-53.1      scales_1.1.1      
[45] hms_1.0.0          promises_1.2.0.1   parallel_4.0.5     RColorBrewer_1.1-2
[49] curl_4.3           yaml_2.2.1         sass_0.3.1         reshape_0.8.8     
[53] stringi_1.5.3      highr_0.8          zip_2.1.1          boot_1.3-27       
[57] rlang_0.4.10       pkgconfig_2.0.3    systemfonts_1.0.1  evaluate_0.14     
[61] lattice_0.20-41    labeling_0.4.2     tidyselect_1.1.0   GGally_2.1.1      
[65] plyr_1.8.6         magrittr_2.0.1     R6_2.5.0           generics_0.1.0    
[69] DBI_1.1.1          foreign_0.8-81     pillar_1.5.1       haven_2.3.1       
[73] withr_2.4.1        abind_1.4-5        modelr_0.1.8       crayon_1.4.1      
[77] utf8_1.1.4         tmvnsim_1.0-2      rmarkdown_2.7      grid_4.0.5        
[81] readxl_1.3.1       CDM_7.5-15         pbivnorm_0.6.0     git2r_0.28.0      
[85] reprex_1.0.0       digest_0.6.27      webshot_0.5.2      httpuv_1.5.5      
[89] stats4_4.0.5       munsell_0.5.0      viridisLite_0.3.0  bslib_0.2.4       
[93] R2WinBUGS_2.1-21

Simulation Study 2

Posterior Convergence

R. Noah Padgett

2022-01-09

Convergence

Summaring Convergence

Factor Loadings (\(\lambda\))

Item Thresholds (\(\tau\))

Latent Response Variance (\(\theta\))

Response Time Intercepts (\(\beta_{lrt}\))

Response Time Precision (\(\sigma_{lrt}\))

Response Time Factor Precision (\(\sigma_s\))

Factor Covariance (\(\sigma_{st}\))

PID Relationship (\(\rho\))

Factor Reliability (\(\omega\))

Effect of Simulated Conditions

Factor Loadings (\(\lambda\))

Item Thresholds (\(\tau\))

Latent Response Variance (\(\theta\))

Response Time Intercepts (\(\beta_{lrt}\))

Response Time Precision (\(\sigma_{lrt}\))

Response Time Factor Precision (\(\sigma_s\))

Factor Covariance (\(\sigma_{st}\))

PID Relationship (\(\rho\))

Factor Reliability (\(\omega\))

Manuscript Tables and Figures (latex formated)

Tables